IN ABC, m<BAC =3x+9, m<ABC =8x+11, and m<BCA= 5x-8. Find the measures of <1,<2,<3. SHow your woek for solving x and finding each angle measure clearly.

IN ABC, m<BAC =3x+9, m<ABC =8x+11, and m<BCA= 5x-8. Find the measures of <1,<2,<3. SHow your woek for solving x and finding each angle measure clearly.
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You know the three angles sum to 180, so

3x+9 + 8x+11 + 5x-8 = 180
16x + 12 = 180
...

Now you can find x, and thus the three angles.

To find the measures of angles <1, <2, and <3 in triangle ABC, we need to find the value of x first.

Given: m<BAC = 3x + 9, m<ABC = 8x + 11, and m<BCA = 5x - 8.

To find x, we can set up an equation by using the fact that the sum of all angles in a triangle is 180 degrees.

<1 + <2 + <3 = 180 (sum of all angles in ABC)

Substituting the given angle measures in terms of x:

(3x + 9) + (8x + 11) + (5x - 8) = 180

Now we can solve for x.

3x + 9 + 8x + 11 + 5x - 8 = 180
16x + 12 = 180
16x = 180 - 12
16x = 168
x = 168/16
x = 10.5

Now that we have found the value of x, we can substitute it back into the angle measures to find the measures of <1, <2, and <3.

<1 = 3x + 9 = 3(10.5) + 9 = 31.5 + 9 = 40.5 degrees
<2 = 8x + 11 = 8(10.5) + 11 = 84 + 11 = 95 degrees
<3 = 5x - 8 = 5(10.5) - 8 = 52.5 - 8 = 44.5 degrees

Therefore, the measures of <1, <2, and <3 are 40.5 degrees, 95 degrees, and 44.5 degrees, respectively.